Volumes of SLn(ℂ)–representations of hyperbolic 3–manifolds
| Autor: | Wolfgang Pitsch, Joan Porti |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Pure mathematics
Finite volume method 010308 nuclear & particles physics 010102 general mathematics Lie algebra cohomology Hyperbolic manifold Rigidity (psychology) Space (mathematics) Mathematics::Geometric Topology 01 natural sciences Characteristic class 0103 physical sciences Geometry and Topology 0101 mathematics Variety (universal algebra) Mathematics Volume (compression) |
| Zdroj: | Geometry & Topology. 22:4067-4112 |
| ISSN: | 1364-0380 1465-3060 |
| DOI: | 10.2140/gt.2018.22.4067 |
| Popis: | Let M be a compact oriented three-manifold whose interior is hyperbolic of finite volume. We prove a variation formula for the volume on the variety of representations of π 1 ( M ) in SL n ( ℂ ) . Our proof follows the strategy of Reznikov’s rigidity when M is closed; in particular, we use Fuks’s approach to variations by means of Lie algebra cohomology. When n = 2 , we get Hodgson’s formula for variation of volume on the space of hyperbolic Dehn fillings. Our formula also recovers the variation of volume on the space of decorated triangulations obtained by Bergeron, Falbel and Guilloux and Dimofte, Gabella and Goncharov. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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